167.23/44.31	YES
167.23/44.33	
167.23/44.33	Problem:
167.23/44.33	 a(b(a(b(x1)))) -> b(b(a(a(x1))))
167.23/44.33	 b(a(b(a(x1)))) -> a(b(a(b(x1))))
167.23/44.33	 b(a(b(b(x1)))) -> a(b(a(a(x1))))
167.23/44.33	
167.23/44.33	Proof:
167.23/44.33	 String Reversal Processor:
167.23/44.33	  b(a(b(a(x1)))) -> a(a(b(b(x1))))
167.23/44.33	  a(b(a(b(x1)))) -> b(a(b(a(x1))))
167.23/44.33	  b(b(a(b(x1)))) -> a(a(b(a(x1))))
167.23/44.33	  Matrix Interpretation Processor: dim=1
167.23/44.33	   
167.23/44.33	   interpretation:
167.23/44.33	    [a](x0) = x0,
167.23/44.33	    
167.23/44.33	    [b](x0) = 2x0 + 3
167.23/44.33	   orientation:
167.23/44.33	    b(a(b(a(x1)))) = 4x1 + 9 >= 4x1 + 9 = a(a(b(b(x1))))
167.23/44.33	    
167.23/44.33	    a(b(a(b(x1)))) = 4x1 + 9 >= 4x1 + 9 = b(a(b(a(x1))))
167.23/44.33	    
167.23/44.33	    b(b(a(b(x1)))) = 8x1 + 21 >= 2x1 + 3 = a(a(b(a(x1))))
167.23/44.33	   problem:
167.23/44.33	    b(a(b(a(x1)))) -> a(a(b(b(x1))))
167.23/44.33	    a(b(a(b(x1)))) -> b(a(b(a(x1))))
167.23/44.33	   DP Processor:
167.23/44.33	    DPs:
167.23/44.33	     b#(a(b(a(x1)))) -> b#(x1)
167.23/44.33	     b#(a(b(a(x1)))) -> b#(b(x1))
167.23/44.33	     b#(a(b(a(x1)))) -> a#(b(b(x1)))
167.23/44.33	     b#(a(b(a(x1)))) -> a#(a(b(b(x1))))
167.23/44.33	     a#(b(a(b(x1)))) -> a#(x1)
167.23/44.33	     a#(b(a(b(x1)))) -> b#(a(x1))
167.23/44.33	     a#(b(a(b(x1)))) -> a#(b(a(x1)))
167.23/44.33	     a#(b(a(b(x1)))) -> b#(a(b(a(x1))))
167.23/44.33	    TRS:
167.23/44.33	     b(a(b(a(x1)))) -> a(a(b(b(x1))))
167.23/44.33	     a(b(a(b(x1)))) -> b(a(b(a(x1))))
167.23/44.33	    TDG Processor:
167.23/44.33	     DPs:
167.23/44.33	      b#(a(b(a(x1)))) -> b#(x1)
167.23/44.33	      b#(a(b(a(x1)))) -> b#(b(x1))
167.23/44.33	      b#(a(b(a(x1)))) -> a#(b(b(x1)))
167.23/44.33	      b#(a(b(a(x1)))) -> a#(a(b(b(x1))))
167.23/44.33	      a#(b(a(b(x1)))) -> a#(x1)
167.23/44.33	      a#(b(a(b(x1)))) -> b#(a(x1))
167.23/44.33	      a#(b(a(b(x1)))) -> a#(b(a(x1)))
167.23/44.33	      a#(b(a(b(x1)))) -> b#(a(b(a(x1))))
167.23/44.33	     TRS:
167.23/44.33	      b(a(b(a(x1)))) -> a(a(b(b(x1))))
167.23/44.33	      a(b(a(b(x1)))) -> b(a(b(a(x1))))
167.23/44.33	     graph:
167.23/44.33	      a#(b(a(b(x1)))) -> a#(b(a(x1))) ->
167.23/44.33	      a#(b(a(b(x1)))) -> b#(a(b(a(x1))))
167.23/44.33	      a#(b(a(b(x1)))) -> a#(b(a(x1))) ->
167.23/44.33	      a#(b(a(b(x1)))) -> a#(b(a(x1)))
167.23/44.33	      a#(b(a(b(x1)))) -> a#(b(a(x1))) ->
167.23/44.33	      a#(b(a(b(x1)))) -> b#(a(x1))
167.23/44.33	      a#(b(a(b(x1)))) -> a#(b(a(x1))) -> a#(b(a(b(x1)))) -> a#(x1)
167.23/44.33	      a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> b#(a(b(a(x1))))
167.23/44.33	      a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> a#(b(a(x1)))
167.23/44.33	      a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> b#(a(x1))
167.23/44.33	      a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> a#(x1)
167.23/44.33	      a#(b(a(b(x1)))) -> b#(a(b(a(x1)))) ->
167.23/44.33	      b#(a(b(a(x1)))) -> a#(a(b(b(x1))))
167.23/44.33	      a#(b(a(b(x1)))) -> b#(a(b(a(x1)))) ->
167.23/44.33	      b#(a(b(a(x1)))) -> a#(b(b(x1)))
167.23/44.33	      a#(b(a(b(x1)))) -> b#(a(b(a(x1)))) ->
167.23/44.33	      b#(a(b(a(x1)))) -> b#(b(x1))
167.23/44.33	      a#(b(a(b(x1)))) -> b#(a(b(a(x1)))) -> b#(a(b(a(x1)))) -> b#(x1)
167.23/44.33	      a#(b(a(b(x1)))) -> b#(a(x1)) ->
167.23/44.33	      b#(a(b(a(x1)))) -> a#(a(b(b(x1))))
167.23/44.33	      a#(b(a(b(x1)))) -> b#(a(x1)) -> b#(a(b(a(x1)))) -> a#(b(b(x1)))
167.23/44.33	      a#(b(a(b(x1)))) -> b#(a(x1)) -> b#(a(b(a(x1)))) -> b#(b(x1))
167.23/44.33	      a#(b(a(b(x1)))) -> b#(a(x1)) -> b#(a(b(a(x1)))) -> b#(x1)
167.23/44.33	      b#(a(b(a(x1)))) -> a#(a(b(b(x1)))) ->
167.23/44.33	      a#(b(a(b(x1)))) -> b#(a(b(a(x1))))
167.23/44.33	      b#(a(b(a(x1)))) -> a#(a(b(b(x1)))) ->
167.23/44.33	      a#(b(a(b(x1)))) -> a#(b(a(x1)))
167.23/44.33	      b#(a(b(a(x1)))) -> a#(a(b(b(x1)))) ->
167.23/44.33	      a#(b(a(b(x1)))) -> b#(a(x1))
167.23/44.33	      b#(a(b(a(x1)))) -> a#(a(b(b(x1)))) ->
167.23/44.33	      a#(b(a(b(x1)))) -> a#(x1)
167.23/44.33	      b#(a(b(a(x1)))) -> a#(b(b(x1))) ->
167.23/44.33	      a#(b(a(b(x1)))) -> b#(a(b(a(x1))))
167.23/44.33	      b#(a(b(a(x1)))) -> a#(b(b(x1))) ->
167.23/44.33	      a#(b(a(b(x1)))) -> a#(b(a(x1)))
167.23/44.33	      b#(a(b(a(x1)))) -> a#(b(b(x1))) ->
167.23/44.33	      a#(b(a(b(x1)))) -> b#(a(x1))
167.23/44.33	      b#(a(b(a(x1)))) -> a#(b(b(x1))) -> a#(b(a(b(x1)))) -> a#(x1)
167.23/44.33	      b#(a(b(a(x1)))) -> b#(b(x1)) ->
167.23/44.33	      b#(a(b(a(x1)))) -> a#(a(b(b(x1))))
167.23/44.33	      b#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(b(a(x1)))) -> a#(b(b(x1)))
167.23/44.33	      b#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(b(a(x1)))) -> b#(b(x1))
167.23/44.33	      b#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(b(a(x1)))) -> b#(x1)
167.23/44.33	      b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(a(b(b(x1))))
167.23/44.33	      b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> a#(b(b(x1)))
167.23/44.33	      b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> b#(b(x1))
167.23/44.33	      b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> b#(x1)
167.23/44.33	     Arctic Interpretation Processor:
167.23/44.33	      dimension: 1
167.23/44.33	      usable rules:
167.23/44.33	       b(a(b(a(x1)))) -> a(a(b(b(x1))))
167.23/44.33	       a(b(a(b(x1)))) -> b(a(b(a(x1))))
167.23/44.33	      interpretation:
167.23/44.33	       [a#](x0) = 1x0,
167.23/44.33	       
167.23/44.33	       [b#](x0) = x0 + 8,
167.23/44.33	       
167.23/44.33	       [a](x0) = 1x0 + 11,
167.23/44.33	       
167.23/44.33	       [b](x0) = x0 + 6
167.23/44.33	      orientation:
167.23/44.34	       b#(a(b(a(x1)))) = 2x1 + 12 >= x1 + 8 = b#(x1)
167.23/44.34	       
167.23/44.34	       b#(a(b(a(x1)))) = 2x1 + 12 >= x1 + 8 = b#(b(x1))
167.23/44.34	       
167.23/44.34	       b#(a(b(a(x1)))) = 2x1 + 12 >= 1x1 + 7 = a#(b(b(x1)))
167.23/44.34	       
167.23/44.34	       b#(a(b(a(x1)))) = 2x1 + 12 >= 2x1 + 12 = a#(a(b(b(x1))))
167.23/44.34	       
167.23/44.34	       a#(b(a(b(x1)))) = 2x1 + 12 >= 1x1 = a#(x1)
167.23/44.34	       
167.23/44.34	       a#(b(a(b(x1)))) = 2x1 + 12 >= 1x1 + 11 = b#(a(x1))
167.23/44.34	       
167.23/44.34	       a#(b(a(b(x1)))) = 2x1 + 12 >= 2x1 + 12 = a#(b(a(x1)))
167.23/44.34	       
167.23/44.34	       a#(b(a(b(x1)))) = 2x1 + 12 >= 2x1 + 12 = b#(a(b(a(x1))))
167.23/44.34	       
167.23/44.34	       b(a(b(a(x1)))) = 2x1 + 12 >= 2x1 + 12 = a(a(b(b(x1))))
167.23/44.34	       
167.23/44.34	       a(b(a(b(x1)))) = 2x1 + 12 >= 2x1 + 12 = b(a(b(a(x1))))
167.23/44.34	      problem:
167.23/44.34	       DPs:
167.23/44.34	        b#(a(b(a(x1)))) -> a#(a(b(b(x1))))
167.23/44.34	        a#(b(a(b(x1)))) -> a#(b(a(x1)))
167.23/44.34	        a#(b(a(b(x1)))) -> b#(a(b(a(x1))))
167.23/44.34	       TRS:
167.23/44.34	        b(a(b(a(x1)))) -> a(a(b(b(x1))))
167.23/44.34	        a(b(a(b(x1)))) -> b(a(b(a(x1))))
167.23/44.34	      Restore Modifier:
167.23/44.34	       DPs:
167.23/44.34	        b#(a(b(a(x1)))) -> a#(a(b(b(x1))))
167.23/44.34	        a#(b(a(b(x1)))) -> a#(b(a(x1)))
167.23/44.34	        a#(b(a(b(x1)))) -> b#(a(b(a(x1))))
167.23/44.34	       TRS:
167.23/44.34	        b(a(b(a(x1)))) -> a(a(b(b(x1))))
167.23/44.34	        a(b(a(b(x1)))) -> b(a(b(a(x1))))
167.23/44.34	       EDG Processor:
167.23/44.34	        DPs:
167.23/44.34	         b#(a(b(a(x1)))) -> a#(a(b(b(x1))))
167.23/44.34	         a#(b(a(b(x1)))) -> a#(b(a(x1)))
167.23/44.34	         a#(b(a(b(x1)))) -> b#(a(b(a(x1))))
167.23/44.34	        TRS:
167.23/44.34	         b(a(b(a(x1)))) -> a(a(b(b(x1))))
167.23/44.34	         a(b(a(b(x1)))) -> b(a(b(a(x1))))
167.23/44.34	        graph:
167.23/44.34	         a#(b(a(b(x1)))) -> a#(b(a(x1))) ->
167.23/44.34	         a#(b(a(b(x1)))) -> a#(b(a(x1)))
167.23/44.34	         a#(b(a(b(x1)))) -> a#(b(a(x1))) ->
167.23/44.34	         a#(b(a(b(x1)))) -> b#(a(b(a(x1))))
167.23/44.34	         a#(b(a(b(x1)))) -> b#(a(b(a(x1)))) ->
167.23/44.34	         b#(a(b(a(x1)))) -> a#(a(b(b(x1))))
167.23/44.34	         b#(a(b(a(x1)))) -> a#(a(b(b(x1)))) ->
167.23/44.34	         a#(b(a(b(x1)))) -> a#(b(a(x1)))
167.23/44.34	         b#(a(b(a(x1)))) -> a#(a(b(b(x1)))) -> a#(b(a(b(x1)))) -> b#(a(b(a(x1))))
167.23/44.34	        Arctic Interpretation Processor:
167.23/44.34	         dimension: 1
167.23/44.34	         usable rules:
167.23/44.34	          b(a(b(a(x1)))) -> a(a(b(b(x1))))
167.23/44.34	          a(b(a(b(x1)))) -> b(a(b(a(x1))))
167.23/44.34	         interpretation:
167.23/44.34	          [a#](x0) = x0 + 0,
167.23/44.34	          
167.23/44.34	          [b#](x0) = 4x0 + 8,
167.23/44.34	          
167.23/44.34	          [a](x0) = x0 + 0,
167.23/44.34	          
167.23/44.34	          [b](x0) = 4x0 + 12
167.23/44.34	         orientation:
167.23/44.34	          b#(a(b(a(x1)))) = 8x1 + 16 >= 8x1 + 16 = a#(a(b(b(x1))))
167.23/44.34	          
167.23/44.34	          a#(b(a(b(x1)))) = 8x1 + 16 >= 4x1 + 12 = a#(b(a(x1)))
167.23/44.34	          
167.23/44.34	          a#(b(a(b(x1)))) = 8x1 + 16 >= 8x1 + 16 = b#(a(b(a(x1))))
167.23/44.34	          
167.23/44.34	          b(a(b(a(x1)))) = 8x1 + 16 >= 8x1 + 16 = a(a(b(b(x1))))
167.23/44.34	          
167.23/44.34	          a(b(a(b(x1)))) = 8x1 + 16 >= 8x1 + 16 = b(a(b(a(x1))))
167.23/44.34	         problem:
167.23/44.34	          DPs:
167.23/44.34	           b#(a(b(a(x1)))) -> a#(a(b(b(x1))))
167.23/44.34	           a#(b(a(b(x1)))) -> b#(a(b(a(x1))))
167.23/44.34	          TRS:
167.23/44.34	           b(a(b(a(x1)))) -> a(a(b(b(x1))))
167.23/44.34	           a(b(a(b(x1)))) -> b(a(b(a(x1))))
167.23/44.34	         Restore Modifier:
167.23/44.34	          DPs:
167.23/44.34	           b#(a(b(a(x1)))) -> a#(a(b(b(x1))))
167.23/44.34	           a#(b(a(b(x1)))) -> b#(a(b(a(x1))))
167.23/44.34	          TRS:
167.23/44.34	           b(a(b(a(x1)))) -> a(a(b(b(x1))))
167.23/44.34	           a(b(a(b(x1)))) -> b(a(b(a(x1))))
167.23/44.34	          EDG Processor:
167.23/44.34	           DPs:
167.23/44.34	            b#(a(b(a(x1)))) -> a#(a(b(b(x1))))
167.23/44.34	            a#(b(a(b(x1)))) -> b#(a(b(a(x1))))
167.23/44.34	           TRS:
167.23/44.34	            b(a(b(a(x1)))) -> a(a(b(b(x1))))
167.23/44.34	            a(b(a(b(x1)))) -> b(a(b(a(x1))))
167.23/44.34	           graph:
167.23/44.34	            a#(b(a(b(x1)))) -> b#(a(b(a(x1)))) ->
167.23/44.34	            b#(a(b(a(x1)))) -> a#(a(b(b(x1))))
167.23/44.34	            b#(a(b(a(x1)))) -> a#(a(b(b(x1)))) -> a#(b(a(b(x1)))) -> b#(a(b(a(x1))))
167.23/44.34	           Bounds Processor:
167.23/44.34	            bound: 0
167.23/44.34	            enrichment: match-dp
167.23/44.34	            automaton:
167.23/44.34	             final states: {1}
167.23/44.34	             transitions:
167.23/44.34	              b0(2) -> 3*
167.23/44.34	              b0(3) -> 4*
167.23/44.34	              f40() -> 2*
167.23/44.34	              a{#,0}(5) -> 1*
167.23/44.34	              a0(4) -> 5*
167.23/44.34	              a0(11) -> 12*
167.23/44.34	              5 -> 11*
167.23/44.34	              12 -> 3*
167.23/44.34	            problem:
167.23/44.34	             DPs:
167.23/44.34	              a#(b(a(b(x1)))) -> b#(a(b(a(x1))))
167.23/44.34	             TRS:
167.23/44.34	              b(a(b(a(x1)))) -> a(a(b(b(x1))))
167.23/44.34	              a(b(a(b(x1)))) -> b(a(b(a(x1))))
167.23/44.34	            Restore Modifier:
167.23/44.34	             DPs:
167.23/44.34	              a#(b(a(b(x1)))) -> b#(a(b(a(x1))))
167.23/44.34	             TRS:
167.23/44.34	              b(a(b(a(x1)))) -> a(a(b(b(x1))))
167.23/44.34	              a(b(a(b(x1)))) -> b(a(b(a(x1))))
167.23/44.34	             EDG Processor:
167.23/44.34	              DPs:
167.23/44.34	               a#(b(a(b(x1)))) -> b#(a(b(a(x1))))
167.23/44.34	              TRS:
167.23/44.34	               b(a(b(a(x1)))) -> a(a(b(b(x1))))
167.23/44.34	               a(b(a(b(x1)))) -> b(a(b(a(x1))))
167.23/44.34	              graph:
167.23/44.34	               
167.23/44.34	              SCC Processor:
167.23/44.34	               #sccs: 0
167.23/44.34	               #rules: 0
167.23/44.34	               #arcs: 0/1
167.23/44.34	               
167.23/44.34	EOF